In the circuit shown the resistance R is kept in a chamber whose temperature. is `20^(@)`C which remains constant. The initial temperature and resistance of R is `50^(@)C` and `15 Omega`respectively. The rate of change of resistance R with temperature is `(1)/(2)Omega//^(@)C` and the rate of decrease of temperature of R is In`(3//100)` times the temperature difference from the surrounding (Assume the resistance R loses heat only in accordance with Newton's law of cooling) If K is closed at t = 0, then find the
(a) value of. R for which power dissipation in it is maximum.
(b) temperature of R when power dissipation is maximum
(c) time after which the power dissipation will be maximum

Explanation

(a) `50Omega`
(b) `30^(@)C`
(c) `100 sec`